I want to assess the three conditions required for instrumental variable estimation in a cross-sectional sample of individuals nested in regions (Bastardoz et al., 2023).
Data-generating process: I am interested in the effect of z on y, conditional on self-selection into treatment x, where y and x are binary variables and z is a categorical nominal variable.
Stata pseudocode:
Problem: To my best knowledge, the standard setup discussed in Bastardoz et al. (2023) is a linear regression, where y is continuous, and x is continuous. I have seen that for binary endogenous x, it is common to use linear IV regression to test for instrument relevance. However, I am uncertain how to test for instrument relevance for nominal instruments and if these tests are available in Stata. For example, should I do a joint F-test for all dummies using linear IV regression or is there a completely different test?
References
Bastardoz, N., Matthews, M. J., Sajons, G. B., Ransom, T., Kelemen, T. K., & Matthews, S. H. (2023). Instrumental variables estimation: Assumptions, pitfalls, and guidelines. The Leadership Quarterly, 34(1), 101673. https://doi.org/10.1016/j.leaqua.2022.101673
Data-generating process: I am interested in the effect of z on y, conditional on self-selection into treatment x, where y and x are binary variables and z is a categorical nominal variable.
Stata pseudocode:
Code:
eprobit y x, entreat(x=z)
References
Bastardoz, N., Matthews, M. J., Sajons, G. B., Ransom, T., Kelemen, T. K., & Matthews, S. H. (2023). Instrumental variables estimation: Assumptions, pitfalls, and guidelines. The Leadership Quarterly, 34(1), 101673. https://doi.org/10.1016/j.leaqua.2022.101673
